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I'm trying to solve a saddle point problem of the following form: Let $(E,\mathcal E,\lambda)$ be a measure space; $p$ be a probability density on $(E,\mathcal E,\lambda)$ and $\mu:=p\lambda$ $W$ be ...

In the most general form, I'm interested in any non-trivial results of the following question. Consider metric space $X$ and $Y$, denote all real valued functions on $X$ and $Y$ as $\mathbb{R}^{X}$ ...

Disclaimer: Please bear with me, the question isn't as complicated as it looks like, but I wasn't able to find any simplification for which no counterexample comes to my find. Let $(E,\mathcal E,\...

In Alfred Galichon's book Optimal Transport Methods in Economics the foollowing result is stated for OT problems on the real line. Theorem 4.3.(i) Assume that $\Phi$ is supermodular. Then the primal ...

Let $F$ be a continuous cdf with full support on $[0,1].$ Let $A$ be a compact subset of $\mathbb{R}$ and $\mathcal{M}$ be the set of measurable functions $\alpha:[0,1]\rightarrow A.$ Let $\bar \alpha ...

We know that the measure of central tendency that minimizes the Lp loss is $\min_c \sum_{i=1}^n |x_i - c|^p$ For $p=1$ (L1 loss), this is the median. For $p=2$ (L2 loss), this is the mean. Both of ...